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IN the past, a positive relationship could be observed in the US between the average earnings yield (earnings/price) of the S&P 500 index and government bond yields.

This relationship has become popular as the ‘Fed model' and states in its strongest form that equities are fairly valued when there is equality between the one-year forward looking earnings yield and the 10-year government bond yield. That implies that once yields rise, equity valuations like PE ratios (the inverse of earnings yield), suffer.

The Fed model seems to be simple common sense. First, stocks and bonds are competing asset classes for investors. When stocks ‘yield' more than bonds, stocks are perceived to be the better choice for investors and vice versa. Second, the government bond yield can be seen as a proxy for the risk-free rate. In the event that the risk-free rate rises, the present value of equity falls and vice versa.

Unfortunately, there is no sound theoretical foundation to explain the relationship. In regards to the first argument, the earnings yield of a stock is not a good proxy for its expected return, and is therefore not a sound comparison against the bond yield.

The second argument only holds if we consider the impact of rising yields in isolation, all else being equal. In reality, rising rates are often accompanied by offsetting factors that actually bode well for equities, and we'll expound on that more later in the article.

The Capital Structure Substitution Theory (CSST) re-specifies the Fed model, and by doing so, puts it on a solid theoretical foundation. It suggests that company supply, rather than investor demand, drives the relationship between the earnings yield and interest rates. By adjusting the company's capital structure (mix of equity and bonds) to maximise earnings per share, company management eventually brings the earnings yield towards an equilibrium, where it should equal the after-tax cost of debt.

From a track record perspective, historically there has actually been, on average, a two per cent gap between the two yields. Recently this gap has widened to three per cent, thus presenting the stock market with a ‘cushion' before increases in bond yields start eating into valuations. As the median Fed forecast for the longer run funds rate is only three per cent, the cushion is sufficiently large enough that higher bond yields (or at least yields that are high enough to a plausible extent) do not need to be negative for equity valuations.

Based on the two ideas that in an efficient society, where the public sector needs to compete for capital, the growth rate of the public sector should be roughly in line with overall economic growth and that providers of capital should receive their fair share, there is an argument for bond yields and nominal GDP growth to trend roughly in line.

Thus normally higher bond yields go along with higher GDP growth. What does that imply for equities? Growth of earnings and dividends per share is positively related to GDP growth, which serves as a positive bulwark against the negative valuation impact from higher bond yields.

Whilst the Fed model and CSST imply that higher bond yields will eventually be negative for forward PE ratios, there currently exists a comfortable cushion that should mitigate the effect of anticipated yield rises.

This is further offset by the positive effects from rising earnings that tend to accompany interest rate rises, since central bankers would only raise rates if the wider economy and corporate backdrop is robust enough to handle them. This leaves us to conclude that modest yield rises can be positive for equities overall – something the historical data pays testament to.

Only once yields rise very decisively, valuations will eventually be negatively affected. That is however not our main scenario – at the moment markets are not even pricing in the median Fed forecast. Our base case remains that US yields rise modestly over the coming years – a pace that shouldn't be threatening to medium-term equity returns.